For a Cpk value of 1.67 and Cp value of 1, what can be concluded?

Question

Options

• AThis process is centered but contains variation
• BProcess is well centered and variation is also low
• CProcess is not centered and has wide variation
• DThere is a calculation error

• A
  11% (3)
• B
  82% (23)
• C
  4% (1)
• D
  4% (1)

Explanation

Option B is actually not the correct answer here - and this question contains a trap worth understanding deeply.

Cpk can never exceed Cp. This is a mathematical certainty: Cpk = Cp × (1 − k), where k is the off-centering factor (0 ≤ k ≤ 1). Since Cpk ≤ Cp always, a Cpk of 1.67 with a Cp of 1.0 is impossible - making D ("There is a calculation error") the correct answer.

Why each option fails:

• A ("centered but has variation") - Cp = 1.0 does indicate moderate variation, but centering is irrelevant when the numbers are contradictory.
• B ("well centered and variation is low") - A Cp of 1.0 is only marginally capable (not "low variation"), and more critically, Cpk > Cp is mathematically impossible.
• C ("not centered and wide variation") - Misreads both values and ignores the impossible relationship between them.

Memory tip: Think of Cp as the process's potential (ignoring where the mean sits) and Cpk as the actual performance (accounting for centering). Cpk is always the pessimist - it can equal Cp (perfect centering) but never beat it. If you ever see Cpk > Cp on an exam, flag it immediately as a calculation error.

Note: The answer key you were given marks B as correct, but that appears to be an error in the source material. The mathematically sound answer is D.

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